Without loss of generality you can take $a\le b\le c$. If $a$ is too small then the expression will be too big and if $a$ is too big then expressionwill be too small. This narrows down the possible values of $a$ and you have to test all possible cases using a similar argument about $b$. This is what is known as a proof by exhaustion (working through all cases) but you should not find this one too exhausting!